Linear Algebra

Shelving Guide: Mathematics

This text has a major focus on demonstrating facts and techniques of linear systems that will be invaluable in higher mathematics and related fields. A linear algebra course has two major audiences that it must satisfy. It provides an important theoretical and computational tool for nearly every discipline that uses mathematics. It also provides an introduction to abstract mathematics.

This book has two parts. Chapters 1–7 are written as an introduction. Two primary goals of these chapters are to enable students to become adept at computations and to develop an understanding of the theory of basic topics including linear transformations. Important applications are presented.

Part two, which consists of Chapters 8–14, is at a higher level. It includes topics not usually taught in a first course, such as a detailed justification of the Jordan canonical form, properties of the determinant derived from axioms, the Perron–Frobenius theorem and bilinear and quadratic forms.

Though users will want to make use of technology for many of the computations, topics are explained in the text in a way that will enable students to do these computations by hand if that is desired.

Key features include:

•Chapters 1–7 may be used for a first course relying on applications

•Chapters 8–14 offer a more advanced, theoretical course

•Definitions are highlighted throughout

•MATLAB® and R Project tutorials in the appendices

•Exercises span a range from simple computations to fairly direct abstract exercises

•Historical notes motivate the presentation

About the Authors

James R. Kirkwood holds a PhD from the University of Virginia. He has had over a dozen mathematics textbooks published on various topics including calculus, real analysis, mathematical biology, and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood–Thomas Theory in mathematical physics. He has been awarded several National Science Foundation grants.

Bessie H. Kirkwood holds PhDs in both mathematics and statistics. She co-authored papers in publications such as the Journal of Algebra and the Journal of Multivariate Analysis. Until retirement, she was a professor of mathematics at Sweet Briar College.